We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a LittlewoodRichardson rule for decomposing tensor products of irreducible representations. The new model is based on the ...

We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibrium model is scalar, under the necessary assumption of spectral stability. Moreover, we obtain nonlinear L asymptotic behavior/sharp decay rate of perturbed weak shocks of general simultaneously symmetrizable relaxatio...

In this paper, we determine derivations of Borel subalgebras and their derived subalgebras called nilradicals, in Kac-Moody algebras (and contragredient Lie algebras) over any field of characteristic 0; and we also determine automorphisms of those subalgebras in symmetrizable Kac-Moody algebras. The results solve a conjecture posed by R. V. Moody about 30 years ago which generalizes a result by...

This paper presents a novel approach to solution-based adaptation for unsteady discretizations of symmetrizable conservation laws. This approach is based on an extension of the entropy adjoint approach, which was previously introduced for steady-state simulations. Key to the approach is the interpretation of symmetrizing entropy variables as adjoint solutions for an output that states the entro...

Let $G$ be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on induced from unramified cusp forms finite-dimensional Levi subgroups of maximal parabolic subgroups. Under natural condition subgroups, we prove that the cuspidal are entire full complex plane.